Power character matrices

Power Hadamard matrices

We introduce power Hadamard matrices, in order to study the structure of (group) generalized Hadamard matrices, Butson (generalized) Hadamard matrices and other related orthogonal matrices, with which they share certain common characteristics. The new objects turn out to be as interesting, and perhaps as useful, as the objects that motivated them. We develop a basic theory of power Hadamard mat...

Character values and decomposition matrices of symmetric groups

The relationships between the values taken by ordinary characters of symmetric groups are exploited to prove two theorems in the modular representation theory of the symmetric group. 1. The decomposition matrices of symmetric groups in odd characteristic have distinct rows. In characteristic 2 the rows of a decomposition matrix labelled by the different partitions λ and μ are equal if and only ...

Deterministic Compressed Sensing Matrices from Additive Character Sequences

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a K×N measurement matrix for compressed sensing is deterministically constructed via additive character sequences. The Weil bound is then used to show that the matrix has asymptotically optimal coherence for N = K, and to present a sufficient condition on the ...

Modeling inverse covariance matrices by expansion of tied basis matrices for online handwritten Chinese character recognition

The state-of-the-art modified quadratic discriminant function (MQDF) based approach for online handwritten Chinese character recognition (HCCR) assumes that the feature vectors of each character class can be modeled by a Gaussian distribution with a mean vector and a full covariance matrix. In order to achieve a high recognition accuracy, enough number of leading eigenvectors of the covariance ...

A note on power bounded matrices